Approximate analytical orbital functions for second and third-row transition metals

Harold Basch, Harry B. Gray

Research output: Contribution to journalArticlepeer-review

239 Scopus citations


Approximate analytical functions for s, p, d, and f orbitals of the second and third-row transition metals have been constructed from the Herman-Skillman Hartree-Fock-Slater numerical wave functions. They consist of orthonormal linear combinations of Slater-type orbital functions, and depend on a weighted least-squares criterion to judge the accuracy of the fit. The option of using a single-μ (one orbital function per extremum) or double-μ representation for the outermost maximum of a given function is included. Whereas the latter basis set is more flexible, convergence problems in the fitting method as well as an inherent arbitrariness in choosing the fitting criterion result in derived parameters which are not uniquely determined by the least-squares criterion alone. By relaxing the orthogonality requirement for orbitals of the same l and different n it is shown that the accuracy of the fit can be significantly improved. The importance of a proper choice for the fitting criterion is discussed.

Original languageEnglish
Pages (from-to)367-376
Number of pages10
JournalTheoretica Chimica Acta
Issue number4
StatePublished - Aug 1966
Externally publishedYes


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